Six dogs have been rescued from a multistorey car park in Liverpool gutted by a fire on Sunday night which destroyed more than 1,000 cars.

Fire investigators said on Monday they did not believe the fire was started deliberately.

The dogs are thought to have been left in the vehicles while their owners attended the Liverpool international horse show at the neighbouring Echo Arena.

Firefighters rescued the animals after extinguishing the “ferocious” fire which whipped through the car park in Kings Dock on New Year’s Eve.

The overwhelming majority of the estimated 1,400 vehicles in the seven-storey structure were destroyed, according to Merseyside’s chief fire officer, Dan Stephens. Just a few on the roof level and at the corners of the building were spared, he added.

Burned out vehicles and the destroyed floor in the carpark at the Liverpool Echo Arena. Photograph: Merseyside Fire and Rescue/EPA

No human nor animal was seriously injured in the blaze. Two people were treated at the scene for minor smoke inhalation, along with a woman who had hurt her hand as she ran from the flames, said Stephens.

No sprinklers were fitted in the building, he said. “Had the car park had sprinklers, that would certainly have suppressed the fire and might even have extinguished the fire,” he said.

The Labour mayor of Liverpool, Joe Anderson, said fire service cuts had contributed to the devastation. He tweeted:

Joe Anderson (@mayor_anderson)

Car Park fire was reported to me at 4.45pm and I was told it was containable,it would have been if we had enough appliances responding,Chief Fire officer confirmed my view that 2 years ago we would have had 8 fire engines from 4 stations responding instead of 2 #cutscost

Stephens told the Guardian that over the course of the fire 12 fire engines attended, along with three aerial appliances and three high volume pumps (two borrowed from neighbouring forces), while 85 firefighters were involved.

Fire investigators believe the fire started shortly after 4.30pm on Sunday, when the engine compartment of a Range Rover Discovery on the second level went up in flames. “There is nothing to suggest it was anything other than an accidental ignition,” said Stephens.

The fuel in the burning cars emitted such heat that firefighters did not have enough water to extinguish the blaze quickly using the water mains, he said.

By the time they had set up a high-volume pump to draw from the Mersey, the building had been engulfed in flames. It took some time before further pumps arrived from Greater Manchester and elsewhere in Lancashire.

“It’s a bit like Grenfell. With these very high temperatures, you were never going to put the fire out without the whole building taking hold. The speed at which the fire spreads means you simply aren’t going to put it out,” said Stephens.

Crews rescued four dogs on Monday from a car on the roof level, he continued. A further two had been rescued from a car on the second floor on Sunday night before the fire fully took hold.

The remains of the car park at the Liverpool Echo Arena. Photograph: Peter Byrne/PA

“It’s fair to say that the owners were very relieved,” said Stephens. “That was one good outcome at least. We are very fortunate that there were no serious injuries, barring a few people with minor smoke inhalation.”

Witnesses described abandoning their vehicles, grabbing possessions and running for their lives after the blaze broke out. Neighbouring flats were also evacuated, with those unable to return or find alternative accommodation housed temporarily in a shelter at a nearby leisure centre.

The fire caused the cancellation of the final day of the horse show on Sunday.

Sue Wright and her husband, former England footballer Mark, were attending, with friends. She said she saw a car with its engine on fire and helped to lead some of the horses to safety.

“It looked like a ball of fire on the front of the car and it was producing a lot of smoke. We just left everything in [our] car – handbags, telephone, cash – and just went. It was all insignificant as long as everyone was OK and we could get the horses out.”

She said of one of her children spotted the fire and smoke and that she called the emergency services before rushing to the stables. She could hear “bangs and popping” as she arrived.

“The water was coming down to ground level as the firefighters were tackling the fire but it was spooking the horses.”

Wright told the grooms to bridle the horses and they managed to get them out through two exits. “Everybody was helping each other out. It was all hands on deck in the stables,” she said.

Crews were first called at 4.42pm and were on the scene eight minutes later.

Kevin Booth, 44, from Manchester, had left his Fiat 500X in the car park as he took his wife, Julie, and 16-year-old daughter, Holly, to see the horse show as a treat.

“The flames and the smoke were unbelievable,” he said. “People were saying that they would just wait and get their cars back.

“I thought: ‘Have you seen the fire? Are you joking?’ It was frightening, we could hear the bangs of car windows exploding.”

Merseyside police have advised anyone affected by the fire to go to the Pullman hotel, Kings Dock, where staff will be able to provide assistance, aided by the British Red Cross.

Anyone whose car was in the car park should not call police but instead contact their insurers, the force said.

A spokeswoman for the Echo Arena said: “All people and horses are safe and secure.”